Аннотация:It is shown that there exists a σ-compact topological group which cannot be represented as a continuous image of a Lindelöf p-group. This result is based on an inequality for the cardinality of continuous images of Lindelöf p-groups. A closely related result is the following: if a space Y is a continuous image of a Lindelöf p-group, then there exists a covering γ of Y by dyadic compacta such that |γ|≤2^ω. We also show that if a homogeneous compact space Y is a continuous image of a cdc-group G, then Y is a dyadic compactum.